At What Point Is the Following Function a Local Maximum $f ( x , y ) = 3 - 10 x + 12 y - 5 x ^ { 2 } - 6 y ^ { 2 }$

question 102

Multiple Choice

At what point is the following function a local maximum? $f ( x , y ) = 3 - 10 x + 12 y - 5 x ^ { 2 } - 6 y ^ { 2 }$

• A) \(( 1,1 )\)
• B) \(( - 1,1 )\)
• C) \(( 3,1 )\)
• D) \(( 0,1 )\)
• E) \(( 1 , - 1 )\)

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Definitions:

Inefficiency

A situation where resources are not used in the best possible way, leading to wastage or less optimal outcomes.

Equilibrium Quantity

The quantity of a good or service at which quantity demanded equals quantity supplied, leading to a stable market condition.

Producer Surplus

The disparity between the price at which sellers are ready to offer a product and the price they actually get.

Price Floor

A government-imposed limit below which prices cannot fall, typically used to ensure that producers can cover their costs.